I would not attempt stripping it from the clipboard, but from the pasted text. If necessary, you could create a scratch document, paste it there, and clear it from the pasted text, then copy that and close the scratch document without saving, then you would have it in the clipboard.
Here is a macro that unlinks all hyperlinks in the first table of a document.
Code:
Sub HyperlinkFieldUnlink()
' Charles Kenyon 2023-01-22
Dim oField As Field
Dim oRange As range
On Error Resume Next
Set oRange = ActiveDocument.Tables(1).range
For Each oField In oRange.Fields
If oField.Type = wdFieldHyperlink Then
oField.Unlink
End If
Next oField
Set oField = Nothing
On Error GoTo -1
Set oRange = Nothing
End Sub